concreg: Concordance regression for survival data

Description

This package implements concordance regression for survival and other outcome data types, where each summand of the log likelihood consists
of a pair of observations. The parameter estimates are estimated log odds of concordance and straightforwardly translate into partial concordance indices.

Arguments

formula

a formula object, with the response on the left of the operator, and the
model terms on the right. The response can be a survival object as returned by the 'Surv' function, or a single variable.

data

a data.frame in which to interpret the variables named in the 'formula' argument.

normalize

if T, weights are normalized such that their sum is equal to the number of events. May speed up or enable convergence if for some variables no weighting is used.

alpha

the significance level (1-α = the confidence level), 0.05 as default.

maxit

maximum number of iterations (default value is 50)

maxhs

maximum number of step-halvings per iterations (default value is 5).
The increments of the parameter vector in one Newton-Rhaphson iteration step are halved,
unless the new likelihood is greater than the old one, maximally doing maxhs halvings.

epsilon

maxstep

specifies the maximum change of (standardized) parameter values allowed
in one iteration. Default value is 2.5.

id

a vector of patient identification numbers, must be integers starting from 1. These IDs are used for computing the
robust covariance matrix. If id=NA (the default) the program assumes that each line of the data set refers to a distinct individual.

offset

specifies a variable which is included in the model but its parameter estimate is fixed at 1.

scale.weights

specifies a scaling factor (a multiplicative constant) for the weights

x

includes covariates in output object

y

includes outcome in output object

print

prints fitting information on the screen

c.risk

competing risk indicator: 0 for end-of-follow-up, 1 for event of interest, 2 for competing event. status variable in formula must
be 0 for censored (by end-of-follow-up or competing event), 1 for event

strata.var

variable for defining strata in stratified analysis

trunc.weights

quantile at which weights are truncated. set to 1 for no weight truncation.

npar

estimation of nonparametric log odds of concordance?

...

further arguments

Details

If Cox's proportional hazards regression model is used in the presence of non-proportional hazards,
i.e., with underlying time-dependent hazard ratios of prognostic factors, the average relative risk
for such a factor is under- or overestimated and testing power for the corresponding regression parameter
is reduced or type-1 error inflated. In such a situation concordance regression provides an alternative, as
it summarizes a time-dependent effect into a scalar estimate that can be interpreted as log odds of concordance.

Concordance regression is conditional logistic regression on all pairs of observations. In each pair, the subject
that dies earlier is assumed to be a case, and the other subject the control. Pairs with equal survival time or covariate vector
are uninformative. Pairs where the shorter time is censored are also not used. To correct for the loss of information due to
censoring, a weighting scheme is used that upweights eligible pairs by inverse probability of censoring, and at the same time
restores the number of pairs at each failure time that would be expected if there was no censoring.

Inference is based on a robust covariance matrix similar to that of Lin and Wei (1989) proposed for the Cox model. Competing
risks can be accommodated by an additional weighting of subjects who experience a competing risk. These subjects remain in the risk
sets, but their weights in the analysis resemble their probability to be still under follow-up (following Fine and Gray, 1999).

Value

coefficients

the parameter estimates

alpha

the significance level = 1 - confidence level

var

the estimated robust covariance matrix

cov.mb

the model-based covariance matrix

iter

the number of iterations needed to converge

n

the number of observations

y

the response

x

the covariates

formula

the model formula

means

the means of the covariates

linear.predictors

the linear predictors

Wald

the global Wald statistic

df

the degrees of freedom

ci.lower

the lower confidence limits

ci.upper

the upper confidence limits

prob

the p-values

call

the function call

W

A matrix with 3 columns and rows according to the number of uncensored failure times. The first column contains the
stratum numbers, the second column the failure times, the third column the weight for each pair at each failure time.

G

A vector containing the probability of censoring for each observation.